The modern solution for the above mentioned planar zeroth order diffractive element is an element that can locally rotate the local input linear polarization by the desired angle and does so by means of a spatially resolved half-wave birefringent element whose birefringence axis is oriented along the bisector of the angle between the input and output linear polarizations. This solution generally rests on the birefringence property of a 0th order subwavelength binary corrugation grating structure defined at the surface of a high refractive index material.
More particularly, the structure of the state of the art consists of a binary, periodic grating of period Λ with essentially vertical walls wherein the grooves substantially have the refractive index of the cover material nc (usually air) and the ridges are made of a high index material having the refractive index ns of the substrate in which the grating is microstructured as a pure surface relief (or corrugation) grating. The period of the grating has to be small enough to avoid the generation of diffraction orders higher than the 0th order in the cover and in the substrate. This imposes the condition (given that ns is larger than nc):
                    Λ        <                  λ                      n            s                                              (        1        )            when the beam incidence is normal to the grating plane and where λ is the wavelength of the light in vacuum. The condition of equality between Λ and λ/ns is named the cutoff condition for the +/−1st orders under normal incidence, and condition (1) under which all diffraction orders except the 0th order do not propagate in the substrate (they are “evanescent”) corresponds to these orders being “below cutoff”, which is equivalent to the grating being called “subwavelength”.
The polarization component of the incident beam having its electric field parallel to the local grating lines is called the TE polarization and the orthogonal polarization component having the electric field normal to the grating lines is the TM polarization, as shown in FIG. 1. The aim for a polarization transformer is to achieve a phase shift of π between the TE and TM polarizations and to have as low as possible losses due to reflection. The grating then acts as a spatially distributed half-wave element, locally mirroring the input electric field with regard to the local orientation of the grating lines. This mirroring can be seen as a rotation of the polarization, where the rotation angle α for a y-axis oriented polarization, after passing through a grating oriented at angle β with regard to the y-axis, is given by:α=2β  (2)
In order to transform a linear polarization into a spatially non uniform polarization, the E-Field has to be turned by a specific angle β at each point within the beam cross section. As represented in FIG. 2, for the example of transforming a linear to a radial polarization, the required direction of the E-Field after the polarizer is equal to the polar angle Θ of the corresponding position in the beam in a polar coordinate system with its centre at the beam centre. The corresponding grating pattern is sketched in FIG. 2. Note that by turning the element by 90°, one can produce azimuthally polarized light from the same incident beam as also represented in this FIG. 2.
The grating has to fulfill the condition β=Θ/2 everywhere over the beam cross-section. This is not possible to achieve with continuous grating lines without accepting a change in the period (as shown in FIG. 2). If this period change is too large regarding the period tolerance of the grating with respect to its phaseshifting property, a suitable segmentation of the element must be made as represented in FIG. 3. The grating design of FIG. 3 geometrically corresponds to the one of FIG. 2 so that this segmented grating transforms a linear polarization into a radial polarization or into an azimuthal polarization as shown in FIG. 2. The lateral arrangement of such grating lines and the phase functions created by such an element, are known in the scientific literature (e.g. Bomzon, Z.; Biener, G.; Kleiner, V. & Hasman, E., “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285-287 (2002)).
In the solution of the state of the art for the grating in a polarization rotating element (described by Lerman G., Levy U., Optics Letters 33, 2782-2784 (2008)), the grating is a pure surface relief grating, i.e. the ridge material is the same as the grating material. It can be shown that in this described solution the 0th order grating mode only has a propagating character, while higher order grating modes are evanescent (chapter 5 in Tishchenko, A., “Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum. Electron., Springer 37, 309-330 (2005)). In such pure relief grating the fundamental TE0 and TM0 modes always have an effective index which is located between the low index nc of the cover and the high index ns of the substrate which implies that either the TE or the TM polarization exhibits notably less than 100% transmission. This will be clearly established later on in the description of the invention.
The requirement of zero diffraction loss in the substrate of high refractive index imposes a corrugation period Λ smaller than λ/ns (see Equation (1)) which is necessarily very small since the condition for a high TE/TM birefringence calls for a large index ns so as to require grooves that are not too deep and too difficult to fabricate. This can be understood from the effective medium theory used in the state of the art: it is known that with so small a period (much smaller than the wavelength in vacuum) the hypothesis of effective medium for the corrugated layer holds; accordingly, the grating modes of order higher than 0th, which are evanescent, are not taken into consideration and the grating layer is treated as a homogeneous layer characterized by an “effective index”. This homogenized grating layer between the cover medium and the substrate medium thus defines a Fabry-Perot filter for each linear polarization component of the incident light beam. In the effective medium theory, the effective index of the homogenized grating layer “seen” by the linear polarization components of the light beam is given by:
                                          n            eff            TE                    =                                                    Dn                s                2                            +                                                (                                      1                    -                    D                                    )                                ⁢                                  n                  c                  2                                                                    ,                                  ⁢                              n            eff            TM                    =                      1            /                                          (                                                      D                                          n                      s                      2                                                        +                                                            (                                              1                        -                        D                                            )                                                              n                      c                      2                                                                      )                                                                        (        3        )            where D is the duty cycle of the grating, calculated as D=Wr/Λ with Wr being the width of the ridges of the grating as shown in FIG. 4A. It is worth noting here that these expressions coincide with the effective index of the 0th order TE0 and TM0 grating modes as calculated by the exact modal theory for an infinitely small period. In FIG. 4B, the curves of the effective indexes of the 0th order grating modes neffTE and neffTM are given in function of D for three cases: ns=1.5, ns=2.5 and ns=3.5. It can be seen that the birefringence effect strongly decreases with a decrease of the substrate refractive index ns; this in turn implies an increase of the grating height needed to accumulate a phase shift of π between the TE0 and TM0 grating modes upon their propagation through the grating corrugation. This is why a high refractive index is selected for the substrate in which the grating is microstructured.
One of the consequences of the period having to be much smaller than the wavelength as required in the solution of the state of the art (ref. to Equation (1)) is that the field transmission and reflection coefficients of the modes at the top and bottom interfaces are essentially real, i.e., their phase is either close to 0 or close to π as implicitly assumed in the effective medium theory. This has the adverse consequence that achieving in a shallow (i.e., fabricable) grating corrugation the three needed conditions of TE and TM Fabry-Perot filters being set at the maximum resonant transmission peak with minimal grating height (i.e. minimal amount of 2π multiples of the phase for one roundtrip of the light in the Fabry Perot) and the transmitted TE and TM fields being π out of phase is in principle impossible for the refractive indexes available in nature at optical frequencies (see the explanation of this in the description of the invention). The solution of the state of the art is therefore a compromise which has to be searched for numerically, for instance with an air cover and a GaAs substrate (ns=3.48) a TE and TM transmission of 86% and 96% respectively at λ=1064 nm with a period as small as 240 nm, i.e., smaller than a quarter of the wavelength, a ridge width of 144 nm and a groove depth of 470 nm (Lerman G., Levy U., Optics Letters 33, 2782-2784 (2008)), i.e., an aspect ratio of 3.2 for the ridges and 4.9 for the grooves, which is extremely difficult to fabricate.
It is to be noted that the reduced overall transmission, caused by the in-principle impossibility to fulfill the conditions for the π-phaseshifted 100% transmissions of the TE and TM Fabry-Perots, can be partly circumvented by depositing an antireflection layer at the top of the grating lines and at the bottom of the grooves as disclosed in Dimitri Mawet, Pierre Riaud, Jean Surdej, and Jacques Baudrand, “Subwavelength surface-relief gratings for stellar coronagraphy,” Appl. Opt. 44, pp. 7313-7321 (2005). This however adds to the fabrication difficulty, and it does not change the requirement of the critical depth and width of the corrugation.
Thus, the grating elements of the prior art used as polarization transformers face at least two problems. First, they are difficult to manufacture because of the small grating period and of the grating profile with a large groove aspect ratio (groove height divided by groove width). Secondly, their power transmission is notably smaller than 100%. This will be better understood in the following description of the invention.
In order to suppress the reflection from a pure relief grating of the prior art represented by the Optics Letter article by G. Lerman et al., document US 2008/130110 A1 discloses an additional 2D subwavelength grating on top of the 1D birefringent polarizing grating, made of a different material as the etched substrate whose function is to act as an Oth order antireflection micro-structured layer at the air side of the form-birefringent grating where the reflection is the larger. This measure does not change the requirement on the critical depth and width of the grooves and requires a second set of layer deposition, lithography and etching processes with critical alignment between 1D and 2D corrugations.